"Modern science relies upon researchers sharing their work so that their peers can check and verify success or failure. But most scientists still don't share one crucial piece of information - the source codes of the computer programs driving much of today's scientific progress." Pretty crazy this isn't the norm yet.

"Do you seriously think it is a good idea for logic bugs to propagate through hundreds of research projects derived from the same code?

The alternative is to have hundreds of research projects derived from hundreds of different codebases, each with its own bag of logic bugs. All code are inherently buggy, and scientists, due to lack of basic training in software engineering (e.g. code reuse, unit test, etc), tend to write buggier code. "

Yes, that's the point.

If you have multiple independent implementations of the same formula, the more chance you have of finding problems with the actual formula.

You do understand that there is a development methodology that's used for designing and writing robust code by implementing with different languages, don't you?

In fact, many modern CPUs have a similar thing where a calculation takes place twice and the results are compared at the end to verify the calculation was correct. What I'm suggesting is that it's analogous to having multiple cleanroom implementations of formula.